Axial flow compressors and some fans feature stages of paired rows of rotors followed by stators. The compressor may consist of many such stages. Due to viscous effects thin regions or boundary layers of low momentum fluid form adjacent to the aerofoil surface. Typically these, are shed from the trailing edge of each aerofoil as wakes which impinge periodically onto the aerofoils of the next downstream row.
FIG. 1 depicts a typical compressor blade. The aerofoil has a leading edge 104 and a trailing edge 106, a suction surface 100 and a pressure surface 102. The pressure on the suction surface is usually lower than that of the pressure surface in normal operation which generates lift and enables the aerofoil to turn the flow through it. For a conventional aerofoil operating in largely subsonic flow the suction surface is generally convex and the pressure surface flat or concave.
The aerofoil shape is characterised by distributions of thickness and camber along its chord extending between the leading and trailing edges. The camber defines the curve of the aerofoil mean line between the suction and pressure surfaces.
Fluid entering the compressor row does so at an inlet flow angle β1, which will vary over the range of operation of the compressor. All angles are measured relative to the axial direction of the engine. The inlet angle can differ from the physical inlet angle of the aerofoil itself, βm,1. In addition, the flow adjacent the leading edge may experience “upwash” which results in the angle of flow impinging onto the leading edge to be different to the bulk inlet flow angle of the fluid. This is shown as β1′. The difference between βm,1 and β1′ is known as incidence. The variation of β1 from the value at the aerofoil design angle is referred to as the inlet flow angle deviation.
Aerodynamic performance for an aerofoil may be recorded as a “loss loop” that plots aerodynamic loss along the ordinate against the inlet flow angle deviation along the abscissa. Typically, at extremes of deviation, the aerodynamic loss will greater than at lesser inlet flow angle deviations.
One definition for the operating range of the aerofoil is to locate the points at positive and negative inlet flow angle deviation at which the aerofoil loss is double that at the design flow condition. Outside this range the aerofoil section is taken to have stalled aerodynamically i.e. the boundary layer will have separated from one of the aerofoil surfaces. Once this happens it is likely the compressor will become aerodynamically unstable and surge.
At the trailing edge 106 the physical exit angle of the aerofoil is shown as βm,2 and the exit angle of the fluid as β2. For a two dimensional flow past an aerofoil the exit flow angle will always be greater than the physical angle and the difference between the two is known as the deviation.
Current compressor aerofoil design is still very much based on steady flow design criteria. FIG. 2 shows a schematic representation of a modern “controlled diffusion” aerofoil, plotting Mach number (on the ordinate) against fractional chord (on the abscissa)—taken from “Compressor Aerodynamics” (N A Cumpsty, Krieger Publishing Company, 2004). In this case the aerofoil is “supercritical”, that is it features transonic flow over part of the suction surface. However, the form of the velocity distribution may be understood to also apply to a blade with wholly subsonic flow over its surfaces.
Since this is a compressor aerofoil, the bulk flow through it diffuses and thus the exit velocity is below that at inlet. The lift sustained by the aerofoil is a function of the area between the suction 2 and pressure 4 surface lines in FIG. 2 is achieved by elevating the free stream velocity over the suction surface such that the free stream velocity on the suction surface accelerates rapidly from the leading edge stagnation point to a peak within the first 30% of the aerofoil chord. Rapid acceleration is achieved by having the maximum thickness and aerofoil camber in the early part of the aerofoil.
The acceleration is such that the boundary layer remains laminar in this region, even for compressor aerofoils with high Reynolds numbers (typically values of a few million are possible, based on aerofoil chord and inlet flow conditions). After this the flow decelerates to the exit velocity. The deceleration is sharp at first, when the boundary layer is relatively thin and can sustain the deceleration without separating. In this region, shortly after peak velocity the boundary layer will typically undergo rapid transition from laminar to turbulent. In some cases this may be via a small, but closed, separation bubble. After transition the now turbulent boundary layer grows as the flow diffuses. As it thickens it becomes less able to sustain diffusion without separation so the diffusion gradient is generally reduced as the trailing edge is approached. A compressor aerofoil exhibits an overall level of deceleration (or diffusion) on the suction surface that is much higher than the deceleration exhibited by a typical turbine aerofoil. Accordingly, the velocity distribution is much more forward loaded to be able to achieve workable diffusion gradients.
For conventional compressor aerofoils in steady flow there is a rapid transition from laminar to turbulent flow on the early suction surface with the boundary layer downstream of the transition point being fully turbulent. In a laminar boundary layer the flow is smooth and proceeds in streamlines roughly parallel to the surface whilst in turbulent flow there is a general mean motion roughly parallel to the surface but there are also rapid, random fluctuations in velocity which can be of the order of a tenth of the main stream velocity. A turbulent boundary layer has a greater drag than a laminar boundary layer which means it grows more rapidly than a corresponding laminar layer.
The fullness of the boundary layer profile may be characterised by its shape factor. Often designated H12, this is defined as the ratio of the values of the displacement and momentum thicknesses. The displacement thickness is the thickness of a fluid layer at the free stream velocity at the edge of the boundary layer which would have a mass flow equal to the total mass flow in the boundary layer, whilst the momentum thickness is the thickness of a fluid layer at the free stream velocity at the edge of the boundary layer which would have a momentum flux equal to the total momentum flux in the boundary layer.
Initial research into unsteady flow effects on compressor aerofoils has shown that the flow field is complex with wakes and vortical flow features generated by upstream blade rows impinging on the following downstream rows. Because of the diffusing nature of the flow in a compressor the wakes mix out relatively quickly and discrete effects from them are usually only seen in the downstream row.
One piece of research (Ottavy et al., ASME GT-2002-30354.) used a flat plate experiment which had a surface velocity distribution representative of a typical compressor aerofoil suction surface. It also had a wake generator upstream of the flat plate which produced unsteady inlet conditions representative of the real compressor environment. There was a resulting complex interaction between incoming wakes and the early part of the suction surface boundary layer but the rear half of the suction surface had a turbulent and, on a time averaged basis, slightly thicker boundary layer than that observed in steady flow conditions. No observations were made that the unsteady flow could be beneficially exploited to reduce aerofoil loss.
A further series of experiments have been conducted on a stator row downstream of a rotor in a low speed research rig at Cambridge University. Results from this have been published by Wheeler et al., ASME GT2006-90892, GT2007-27802 and GT2008-50177; and by Goodhand and Miller ASME GT2009-59205. These examined the interaction of the unsteady flow with the leading edge geometry of the stator, and the subsequent development of the suction surface boundary layer. Depending on the severity of the interaction of incoming wakes with the leading edge, this turbulent boundary layer was periodically thickened, above the value that would be seen in steady flow. Shaping of the leading edge reduced these effects. However, the boundary layer on the late suction surface was found to remain turbulent.
The unsteady effects are described in more detail in FIG. 3, taken from Wheeler et at ASME GT2006-90892. This presents a time-space diagram showing the time-varying (periodic) boundary layer states for the suction surface of a mid-height section of a stator aerofoil tested in a low speed research compressor. The fractional distance along the aerofoil chord from the leading edge to the trailing edge is given along the abscissa axis and time values (t) given along the ordinate axis have been normalised by the period of wake passing (τ) over the aerofoil.
The particular aerofoil, which has a circular leading edge, exhibits a strong unsteady interaction at the leading edge with the incoming wake. As described previously, in steady flow the early suction surface boundary layer would be expected to be laminar. With the incoming wake this is still the case, but it is thickened as the wake impinges onto the leading edge. The thickened laminar boundary layer quickly undergoes transition to turbulent—even before peak Mach number—which is quite different from steady flow. The turbulent patch propagates along the suction surface with the front of travelling at about 0.7V and the rear at about 0.5V, where V is the freestream velocity at the edge of the boundary layer. Thus in the time-space diagram it is seen to widen as it moves along the suction surface. Wheeler et al. describe this region as “old turbulence”, since it is initiated by the wake at the leading edge.
This region of old turbulence is differentiated into two parts: there is a thickened boundary layer structure (B) that propagates at the front of this turbulent region with the rear of this structure is shown travelling at 0.6V, and behind region B there is a more conventional turbulent boundary layer.
Behind the old turbulence, at least on the early part of the suction surface, a “calmed” region forms which is relatively thinner and similar to the (steady) flow laminar region. Neither of these persist much beyond mid perimeter as they undergo transition to turbulent. Wheeler et al. call this “new turbulence”.
Practically, the boundary layer at the trailing edge is dominated by the old turbulence. The thickness fluctuates periodically and is greater than that which would be seen in steady flow—for which reason the aerofoil loss is correspondingly elevated above the steady flow value.